{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Tutorial 03 - Linear algebra" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Basic linear algebra operations, direct methods for solving linear equation systems, forward and backward substitution, Gaussian elimination, LU decomposition, Thomas algorithm." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import scipy.linalg as la" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Basic operations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Scalar product\n", "\n", "The [scalar product](https://en.wikipedia.org/wiki/Dot_product) of two vectors $ x \\in \\mathbb{R}^{n} $ and $ y \\in \\mathbb{R}^{n} $ is defined as \n", "\n", "$$\n", "x \\cdot y = \\sum_{i=0}^{n-1} x_i y_i.\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "